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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 205700.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205700.m1 | 205700n1 | \([0, 0, 0, -84700, -9483375]\) | \(151732224/85\) | \(37645671250000\) | \([2]\) | \(806400\) | \(1.5521\) | \(\Gamma_0(N)\)-optimal |
205700.m2 | 205700n2 | \([0, 0, 0, -69575, -12977250]\) | \(-5256144/7225\) | \(-51198112900000000\) | \([2]\) | \(1612800\) | \(1.8987\) |
Rank
sage: E.rank()
The elliptic curves in class 205700.m have rank \(0\).
Complex multiplication
The elliptic curves in class 205700.m do not have complex multiplication.Modular form 205700.2.a.m
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.